35 business mathematics in canada 7e exercise 103

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Unformatted text preview: monthly payments of PMT is Same I/Y, P/Y, C/Y, FV 276 N 1 − ( 1 + i ) −n PV = PMT 1 PMT i CPT PV Ans: –131.34 1 − 1.00625 −276 = PMT 0.00625 = 131.34PMT Same I/Y, P/Y, C/Y The PV at age 55 of this amount is PV = FV ( 1 + i ) −n = 131.34PMT (1.00625 ) −60 = 90.37PMT Hence, the pension-at-age-55 option has a 119.24 PMT − 90.37 PMT × 90.37 PMT 100% = 31.9% higher economic value Chapter 10: Ordinary Annuities: Future Value and Present Value 60 N 0 PMT 131.34 FV CPT PV Ans: –90.37 57 Exercise 10.3 (continued) 41. a. Given: For Annuity A, PMT = $100; i = 8%; n = 20 For Annuity B, PMT = $100; i = 8%; n = 40 PVB $1192.46 = (i) = 1.2145 PV A $981.81 Therefore, PVB is 21.45% larger than PVA . FVB $25,905.65 = (ii) = 5.6610 FV A $4576.20 Therefore, FVB is 466.10% larger than FVA . b. Given: For Annuity A, PMT = $100; n = 30; i = 8% For Annuity B, PMT = $100; n = 30; i = 9% PVB $1027.37 = (i) = 0.9126 PV A $1125.78 Therefore, PVB is (1 – 0.9126)× 100% = 8.74% smaller than PVA . FVB $13,630.75 = (ii) = 1.2032 FV A $11,328.32 Therefore, FVB is 20.32% larger than FVA . 58 Business Mathematics in Canada, 7/e Exercise 10.4 % 1. Given: PMT = $2000, i = 72 = 3.5%, 7 I/Y P/Y 2 ENTER (making C/Y = P/Y = 2) 10 N 2000 PMT 0 FV CPT PV Ans: –16,633.211 n = 10, d = 2(5) = 10 1 − (1 + i ) − n PMT PV(5 years from now) = i 1 − 1.035 −20 = $2000 0.035 = $16,633.211 PV(today) = FV (1 + i ) − d = $16,633.211 (1.035 ) −10 = $11,791.60 Same I/Y, P/Y, C/Y 10 N 0 PMT 16633.211 FV CPT PV Ans: −11,791.60 3. Given: PMT = $500, i = 9% = 0.75%, 12 n = 12(3.5) = 42, d = 12(2.75) = 33 1 − (1 + i ) − n PMT PV(2.75 years from now) = i −42 1 − 1.0075 = $500 0.0075 = $17,956.856 PV(today) = FV (1 + i ) − d = $17,956.856 (1.0075 ) −33 = $14,032.77 9 I/Y P/Y 12 ENTER (making C/Y = P/Y = 12) 42 N 500 PMT 0 FV CPT PV Ans: –17,956.856 Same I/Y, P/Y, C/Y 33 N 0 PMT 17956.856 FV CPT PV Ans: −14,032.77 An investment of $14,032.77 today will support the deferred annuity payments. Chapter 10: Ordinary Annui...
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This document was uploaded on 02/08/2014.

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